1. Field of the Invention
The present invention relates to a transmission electron microscope. In particular, the present invention relates to a transmission electron microscope and an image observing method using the same. More specifically, the present invention relates to an observing method which improves the quality of an electron microscope image obtained by a transmission electron microscope having a highly bright and coherent electron source.
2. Description of the Related Art
A transmission electron microscope which is a device illuminating a sample by an electron beam and forming a magnified image by electron lenses with a transmitted electron beam, enables us to directly observe fine structures in the sample. The transmission electron microscope now has an atomic level spatial resolution and has become one of standard measuring instruments in nanotechnology. The transmission electron microscope is also an essential device for analyzing the fine structure of various materials in various fields in the science and the industry; not only in the material science (including semiconductors and metals) but also in the medical and biological research fields. In recent years, the field emission electron guns (FEGs) which provide extremely bright and coherent electron beam are becoming available. Expectation for electron microscopes equipped with FEG has been increased as a means for analyzing and evaluating fine structures from order of microns to atomic scale.
FIG. 1 schematically shows a standard electron optical diagram of a general transmission electron microscope. An electron beam emitted from an electron source 1 is adjusted to have preferable brightness and divergence angle by an illuminating lens 2 and illuminate a sample 3. The transmitted and scattered electron beams 4 transmitted from the sample 3 are incident on an objective lens 5 and selected by an objective aperture 7 located at the back focal plane 6 of the objective lens 5. A magnified image is formed on an objective lens image plane 8. This image is finally magnified to a degree of ten thousand times to million times by an enlarging lenses 9 placed at the later stage and projected on a screen 10. The operator observes this image.
FIG. 2 shows electron optical diagram around the objective lens 5 when the sample can be regarded as a weak phase object (thickness of a sample is sufficiently small that only the electron's phase changes while the its intensity is unchanged after transmitting the sample). When a wavelength of an incident electron beam 11 is λ and a size of the structure in the sample 3 to be observed by the operator is d (namely, selected spatial frequency is 1/d), the scattered wave 4 is emerged from the lower surface of the sample having a scattering angle α=λ/d 12 for an optical axis, and incident on the objective lens 5. If the objective lens cause no spherical aberration, the scattering beam 4 passes through a path indicated by a solid line 13 at the rear of the objective lens 5 to reach to position 14 in the image plane 8. With the influence of the spherical aberration, the scattered wave 4 incident on the objective lens 5 deflected by an extra lens effect due to the spherical aberration. As a result, the electron beam path is shifted from the solid line 13 to a solid line 15 and reaches to a position 16 in the image plane 8. In this case, it is imaged on a position different from the original position in the sample. A position deviation amount 18 obtained by converting a spatial position deviation amount 17 on the image plane 8 to the sample plane gives ambiguity of position information of the image obtained in the device. Since a superimposed image is formed, image interpretation is complicated.
The electron beam influenced by the spherical aberration indicated by the solid line 15 causes an optical path difference 19 (=χ(d)) expressed by Equation 9 using a spherical aberration coefficient Cs and a defocus amount Δf (the insufficient focal state is positive) of the objective lens.
                              χ          ⁡                      (            d            )                          =                                            1              4                        ·            Cs            ·                                          (                                  λ                  d                                )                            4                                -                                                    1                2                            ·              Δ                        ⁢                                                  ⁢                          f              ·                                                (                                      λ                    d                                    )                                2                                                                        [                  Equation          ⁢                                          ⁢          9                ]            Where χ(d) is an optical path difference, Cs is a spherical aberration coefficient of an objective lens, λ is a wavelength of an electron beam, d is size of the structure to be observed, and Δf is a defocus length for an objective lens.
When one divides optical path difference 19 by the λ and multiply by 2π, one gets the phase of electron beam. Sine function of this phase, i.e. Equation 10 is called an aberration function of the objective lens. The chart in FIG. 3 shows the example of the aberration function.
                    Sin        ⁡                  [                                                    2                ⁢                π                            λ                        ·                          χ              ⁡                              (                d                )                                              ]                                    [                  Equation          ⁢                                          ⁢          10                ]            
This function indicates the contrast relative to the background when the transmitted electron beam, which is in parallel with the optical axis passing through the lens center, and the scattered beam are interfered to form an image on the image plane. When the relative contrast is positive, the image is light. When the relative contrast is negative, the image is dark.
The phase contrast transfer function (PCTF) is obtained by multiplying an aberration function of Equation 11 by an envelop function Ed (Δ, d) dependent on a focal length variation Δ of the objective lens shown in Equation 12 and FIG. 4 and an envelop function Ej (β, Δf, d) dependent on a divergence angle β of the electron beam applied on the sample and the defocus length Δf of the objective lens shown in Equation 13 and FIG. 5. Actually, the PCTF generally exhibits the resolution performance of the electron microscope to the spatial frequency 1/d (Equation 14 and FIG. 6).
                    Sin        ⁡                  [                                                    2                ⁢                π                            λ                        ·                          χ              ⁡                              (                d                )                                              ]                                    [                  Equation          ⁢                                          ⁢          11                ]                                                      E            d                    ⁡                      (                          Δ              ,              d                        )                          =                  exp          ⁡                      [                          -                                                                    π                    2                                    ·                                      Δ                    2                                    ·                                      λ                    2                                                                    4                  ⁢                                      d                    4                                                                        ]                                              [                  Equation          ⁢                                          ⁢          12                ]            where Ed (Δ, d) is an envelop function caused by a focal length variation Δ of an objective lens, Δ is a focal length variation of an objective lens, λ is a wavelength of an electron beam, and d is a distance or spatial size between any two selected points.
                                          E            j                    ⁡                      (                          β              ,                              Δ                ⁢                                                                  ⁢                f                            ,              d                        )                          =                  exp          ⁡                      [                          -                                                                    π                    2                                    ·                                                                                    β                        2                                            ⁡                                              (                                                                              Cs                            ·                                                          λ                              2                                                                                -                                                                                                                    d                                2                                                            ·                              Δ                                                        ⁢                                                                                                                  ⁢                            f                                                                          )                                                              2                                                                    d                  6                                                      ]                                              [                  Equation          ⁢                                          ⁢          13                ]            where Ej (β, Δf, d) is an envelop function due to the beam divergence of an incident electron, β is a divergence angle of the beam, λ is a wavelength of the electron beam, d is a distance or spatial size between any two selected points, and Δf is a defocus amount of an objective lens.
                    PCTF        =                              Sin            ⁡                          [                                                                    2                    ⁢                    π                                    λ                                ·                                  χ                  ⁡                                      (                    d                    )                                                              ]                                ·                                    E              d                        ⁡                          (                              Δ                ,                d                            )                                ·                                    E              j                        ⁡                          (                              β                ,                                  Δ                  ⁢                                                                          ⁢                  f                                ,                d                            )                                                          [                  Equation          ⁢                                          ⁢          14                ]            
The focal length variation of an objective lens Δ is expressed by Equation 15 using a chromatic aberration coefficient Cc of the electron microscope, an accelerating voltage stability ΔV/V, an objective lens exciting current stability ΔI/I, and a spread of energy ΔE in an electron beam to an accelerating voltage V.
                    Δ        =                  Cc          ⁢                                                                      (                                                            Δ                      ⁢                                                                                          ⁢                      V                                        V                                    )                                2                            +                                                (                                                            2                      ⁢                      Δ                      ⁢                                                                                          ⁢                      I                                        I                                    )                                2                            +                                                (                                                            Δ                      ⁢                                                                                          ⁢                      E                                        V                                    )                                2                                                                        [                  Equation          ⁢                                          ⁢          15                ]            where Δ is a focal length variation of an objective lens, Cc is a chromatic aberration coefficient of an objective lens, ΔV/V is an accelerating voltage stability, ΔI/I is an objective lens current stability, and ΔE/V is a spread of energy in an electron beam to an accelerating voltage V.
A theoretical resolution which is also called a Scherzer resolution (see O. Sherzer, Journal of Applied Physics 20 (1949) p20) dlim of the electron microscope is defined by Equation 16 using the wavelength λ of the electron beam and the spherical aberration coefficient Cs.dlim=0.66·Cs0.25·λ20.75  [Equation 16]where dlim is the Scherzer resolution, Cs is a spherical aberration coefficient of an objective lens, and λ is a wavelength of an electron beam.
A defocus amount Δfsh of the objective lens to achieve the Scherzer resolution is called a Scherzer focus and is a defocus amount generally providing the highest performance of the device.
When the focal length variation Δ of the objective lens is relatively large as usual with the thermal emission electron beam, the beam coherence is low and PCTF at Scherzer focus will has the shape as shown in a graph of FIG. 7. In this case, PCTF is rapidly attenuated with increase in the spatial frequency 1/d corresponding to the attenuations of both the envelop functions Ed (Δ, d) and Ej (β, Δf, d), becomes so small at the spatial frequency 1/d0 where the PCTF crosses 0 for the first time and later. Therefore it is difficult to obtain information small than the size d0.
On the other hand, when we use the field emission electron beam having high coherency, PCTF at Scherzer focus becomes as shown in FIG. 8 and its attenuation is shifted to the higher spatial frequency side. Therefore information in the high spatial frequency component is contributed to form the image so as to obtain high resolution.
In the region of the spatial frequency 1/d0 and larger, the PCTF is largely oscillated between positive and negative values to the slight change of the spatial frequency. In particular, the positive peak at the spatial frequency 1/dinv indicates that the scattered beams in this peak have an influence on the image with considerable amplitude and incorrect (reversed) phase. Because of the spherical aberration of the objective lens, the scattered electron beams reach at the image plane with some displacement from the correct position, and cause inaccuracy in the image. This is so-called a false image effect. To avoid this effect, we conventionally use an objective aperture to block the scattered electron beam with larger spatial frequency than 1/d0.